Concept

Riemann integral

Related publications (35)

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

We give an extension of Le's stochastic sewing lemma. The stochastic sewing lemma proves convergence in

L_m

of Riemann type sums

\sum _{[s,t] \in \pi } A_{s,t}

for an adapted two-parameter stochastic process A, under certain conditions on the moments o ...

Cambridge Univ Press2024

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

The 2021 Magnonics Roadmap

Dirk Grundler, Thomas Yu, Heena Yang, Joyeeta Sinha

Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research p ...

2021

Constraint-aware neural networks for Riemann problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtai ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Embedded Microchannel Cooling for High Power-Density GaN-on-Si Power Integrated Circuits

Elison de Nazareth Matioli, Remco Franciscus Peter van Erp, Luca Nela, Georgios Kampitsis, Reza Soleiman Zadeh Ardebili

In this work, we demonstrate a new thermal management approach for direct cooling of GaN-on-Si power integrated circuits (ICs), in which the Si substrate functions as a microfluidic heat sink, turning Si into a cost-effective, high thermal performance subs ...

IEEE2020

MATHICSE Technical Report: Constraint-Aware Neural Networks for Riemann Problems

Jan Sickmann Hesthaven, Deep Ray

MATHICSE2019

Photoinitiator-free multi-photon fabrication of compact optical waveguides in polydimethylsiloxane

Demetri Psaltis, Christophe Moser, Giulia Panusa, Ye Pu, Jieping Wang

Compact, low loss flexible optical waveguides are crucial in optofluidic and microfluidic devices for a dense integration of optical functionalities. We demonstrate the fabrication of compact optical waveguides in polydimethylsiloxane through multiphoton l ...

OPTICAL SOC AMER2019

Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation

Jiri Vanicek, Seonghoon Choi, Julien Roulet

Exact nonadiabatic quantum evolution preserves many geometric properties of the molecular Hilbert space. In the first paper of this series ["Paper I," S. Choi and J. Vaníček, J. Chem. Phys. 150, 204112 (2019)], we presented numerical integrators of arbitra ...

2019

Central limit theorems for multilevel Monte Carlo methods

Sebastian Krumscheid, Hakon Andreas Hoel

In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo MLMC estimators, and we provide near optimal weaker conditions under which the CLT is achieved. In ...

2018

Photoinitiator-free Laser Fabrication of Ultra-compact, Low-loss Waveguides in Polydimethylsiloxane

Demetri Psaltis, Christophe Moser, Giulia Panusa, Ye Pu, Jieping Wang

Owing to its excellent elasticity, wide spectral range of transparency, and outstanding chemical and thermal stability, polydimethylsiloxane (PDMS) is an elastomer of great technological importance, being widely used in the fabrication of microfluidic and ...

SPIE-INT SOC OPTICAL ENGINEERING2018

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An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Toyomu Matsuda

We give an extension of Le's stochastic sewing lemma. The stochastic sewing lemma proves convergence in

L_m

of Riemann type sums

\sum _{[s,t] \in \pi } A_{s,t}

for an adapted two-parameter stochastic process A, under certain conditions on the moments o ...

Cambridge Univ Press2024